Particle in a self-consistent field some exact solutions

Models are constructed for the interaction of a quantum-mechanical particle with a scalar self-interacting field for which it has been possible to find exact solutions in an associated problem of a particle in a self-consistent field. It is shown that the condition of regularity of the procedure of expansion with respect to the reciprocal coupling constant in the classical solution in the scheme of collective coordinates is not connected with a large value of the energy of the system in the self-consistent field approximation. The excitation spectrum of the particle in a massive field in symmetric cases and near a state with degenerate vacuum is considered.